NBSIR 75-787

Piezo- and Pyroelectric

Properties of Electrets

Martin G. Broadhurst and G. Thomas Davis

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

October 1975

Final - January 1, 1975 - December 31, 1975

Prepared for Office of Naval Research

Chemistry Program

Arlington, Va. 22044

NBSIR 75-787

PIEZO- AND PYROELECTRIC

PROPERTIES OF ELECTRETA

Martin G. Broadhurst and G. Thomas Davis

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

October 1975

Final - January 1, 1975 - December 31, 1975

Prepared for Office of Naval Research

Chemistry Program

Arlington, Va. 22044

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

PIEZO- AND PYROELECTRIC PROPERTIES

. G. Broadhurst and G. T. Davis

National Bureau of Standards

Washington, D, C. 20234

4. Piezoelectric and Pyroelectric Properties

Introduction

4 . 1 Thermodynamics

4.2 Electret Description

4.21 Preparation of a polar electret

4.22 Real Charges

4.23 Dipole Charges

4.3 Tensor Rotation

4.4 Structure

4.4.1 General

4.4.2 Amorphous Polymers

4.4.3 Semicrystalline Polymers

4.4.4 Molecular Structure

4.4.5 Bulk Structure

4.4.6 Crystal Phases

4.5 Properties

4.5.1 Crystal Relaxations

4.5.2 Ferroelectricity

^.5.3 Space Charges

4.6 Measurements and Data

4.7 Dipole Model for Semicrystalline Polymers

4.8 Summary and Conclusions

Oliver Heavside [4.1] in 1892, postulated that certain waxes would form

permanently polarized dielectrics when allowed to solidify from the molten state

in the presence of an electric field. He viewed an electret as the electrical

analog of a magnet, that is, as having a frozen- in, relatively long lived

(compared to the observation time) non-equilibrium electric dipole moment.

Present popular usage has expanded this concept of an electret to include

monopolar dielectrics having a net frozen-in real charge. Fcr example, the

commercial electret microphone employs a monopolar polymer film. Wax and rosin

electrets were made and studied by EGUCHI in the early 1920' s [4.2].

It was well understood by 1927 [4.3] that molecules containing permanent

electric moments orient in the direction of an electric field when mobile in the

liquid state. Upon solidification of the material in the presence of the field,

the dipoles lose their mobility while retaining their preferred orientation. The

net dipole orientation produces the electret' s permanent polarization (net dipole

moment per unit volume).' It was also recognized that in addition to the electret 's

moment there were also real charges, generally concentrated near the electret

surfaces, which were injected during the formation process by field emission, gas

breakdown or similar processes.

In 1927 piezoelectricity and pyroelectricity were shown theoretically and

experimentally to be properties exhibited by electrets with preferentially ordered

dipoles [4.3, 4]. However, these early wax electrets had poor mechanical strength

and low sensitivity, and applications for them did not develop. More recently,

strong, highly active polymer films, notably poly (vinylidenefluoride) , PVF^,

poly (vinylf luoride) , PVF, and poly (vinylchloride) , PVC, have been recognized

for their potential value as thermoelectric and thermonechanical transducer

materials. Already these materials are finding their way into a new technology
2

of polymer transducers. Japanese scientists have been particularly active in

the early research and development of these devices with the work of FUKADA on

natural and synthetic polymers [4.5], KAWAI who pointed out how general the

effect is [4.6], HAYAKAWA and WADA with their theoretical analyses [4.7] and

industrial scientists who are developing films [4.8, 9] and using them for

various devices [4.10-12]. Host of the polymer electret work in the U.S. lias

focused on using the pyroelectric response for electromagnetic radiation detection

[4.13-21].

In the following sections we shall present concepts, models, experimental

considerations, results, and implications which have resulted from some of the

work on piezoelectric and pyroelectric polymers. This approach is intended to

provide the reader with basic physical concepts needed to identify important

molecular and material parameters, deduce guide-lines for optimizing desirable

properties and provide a basis for selecting new applications.

4.1 Thermodynamic Definitions

Piezo- and pyroelectricity are defined in a formal way by thermodynamics

[4.22]. The piezoelectric constant , is a tensor component given by a second

derivative of the Gibbs free energy with respect to the electric field vector

E and stress tensor T.

3 2 G(E, T 5 T)

9E 3T. l m j

(4.1)

We define a material as being piezoelectric if this second derivative has a

value large enough to be measurable. A material is pyroelectric if at least one

of the components of the pyroelectric coefficient vector p_ defined as

~9 2 G(E, T, T)~

m 3E 3T

L m

(4.2)
- 3

-

has a value large enough to be measurable. Being second derivatives of free

energy, these coefficients have a basis in common with better known quantities

such as coefficients of expansion, compressibility, heat capacity and dielectric

constant and can therefore be expected to be complex quantities if measured

with an alternating stress or show relaxational behavior in the time domain.

The second derivatives in (4.1) and (4.2) can be taken in any order so that

we have,

d . = (3D /3T.)_ v = (3S./3E )_ „ (4.3)

HVJ m j T,E j m T_, T

and

In the above, j=l,...6; m=l, 2, 3; T=stress; S=strain; D=electric displacement;

E=electric field; T=temperature; E=entropy.

The d are often called piezoelectric strain constants whereas the piezoelectric stress constants, e, arise from taking S rather than T_ as the independent

variable in (4.1).

Two other piezoelectric constants h and g can be defined by taking D and

S and D and T_ as independent variables in (4.1), [4.23]. Before relating the

quantities defined in (4.3) and (4.4) to measured quantities, it is well to

develop a better description of an electret and understand the influence of

real and dipolar charges.

4.2 Physical Description of an Electret

4.2.1 Preparation

Consider a slab of polymer which we take to be amorphous, homogeneous,

and elastically isotropic. We first evaporate metallic electrodes on both

sides to eliminate air gaps between the polymer and metal, and then follow the
- 4

-

temperature-voltage- time sequence shown schematically in Fig. 4.1: 1) raise

the temperature from room temperature T to an elevated temperature which we

show here as being above the glass transition temperature, T ; 2) apply a dc

voltage, $ of a few kilovolts resulting in an electric field of several hundred

kilovolts per centimeter of slab thickness, s, between the electrodes; 3) while

maintaining this voltage, lower the temperature back to T^. The electret thus

formed can be represented schematically as shown in Fig. 4.2.

The above poling procedure typically introduces both real and dipolar

charges, and these will affect the behavior of the electret in different ways.

To explain this difference we will consider the two types of charge separately.

4.2.2 Real Charges - Monopolar Electrets

In general, real charges do not contribute to a piezo- and pyroelectric

response as long as the sample is strained uniformly [Ref.4.7, Sec. 2.2]. To

illustrate this fact, consider the example of Fig. 4.3. A slab of dielectric

with relative permittivity k, thickness s and short circuited contact electrodes

contains a layer of trapped positive charges at a distance, x, from the bottom

electrode. The charge densities on the bottom and top electrodes are a and o

° OS

and the charge density of the trapped charge is a . Using Gauss' theorem to

calculate the field due to a plane of charge, the difference between the surface

charge densities on the two electrodes, Aa, is

Aa = a - a = a (1- 2x/s) (4.5)

O S X

If the material is strained so that the distances x and s change to x + Ax and

s + As, then the difference in surface charge Aa becomes:

Aa = a [1 - 2(x + Ax)/(s + As)] = a [1 --(2x/s)(l + Ax/x)/(l + As/s)] (4.6)
- 5 -

If the strain is uniform so that Ax/x = As/s then Ao' = Aa and no charge will

flow as a result of pressure and temperature changes which produce the strain.

This result has been experimentally verified in our laboratory by measurements

on electron-beam-irradiated, fluorinated ethylene-propylene copolymers and by

measurements on samples at varying times after poling when their real charge

content was decaying rapidly. In neither case was there a significant piezoand pyroelectric response attributable to real charge.

Although the homogeneous monopolar electret is generally not piezo- or

pyroelectric it still has considerable value in transducer devices such as

strain sensitive cables and electret microphones. We will describe this effect

in order to clarify the distinction between it and a dipolar electret behavior.

Figure 4.4 shows a schematic diagram of a polymer film which contains real

charges trapped in the polymer matrix (monopolar electret). The film is mounted

so that an air gap separates it from a conductive plate. As the charged film

moves with respect to the plate (under the influence of sound waves, for example)

the plate potential changes and charges flow between it and a conductive contact

electrode on the film through an appropriate circuit. A good polymer for these

devices is fluorinated ethylene-propylene copolymer [4.24, 25]. This same effect

is probably a source of electrical signals generated in flexible polymer- insulated

coaxial cable when it is subjected to mechanical vibrations or pressure changes.

Note that the electret microphone system does not undergo uniform strain. That

is, the air gap is strained much more than the polymer film and hence the real

charges do contribute to current flow. This result suggests the possibility

that artificial piezoelectrics could be made from alternate layers of material

of different compressibility with appropriate charges trapped at the interfaces.

It has been proposed that such a mechanism may be responsible for piezoelectricity

in polyvinylidene fluoride, as will be discussed in Subsect. 4.5.4.
- 6 -

4.2.3 Dipolar Electret

To illustrate the electret' s piezoelectric and pyroelectric behavior

consider Fig. 4.5 and 4.6. As the electrically short-circuited electret contracts

due to an increase in hydrostatic pressure or a decrease in temperature the metal

electrodes move closer to the dipoles and the zero potential is maintained by a

flow of charge. This model of a strain sensitive electret is similar to that

given by Adams [4.3] and accounts for most of the response of piezoelectric and

pyroelectric polymers. Note that the model predicts the direction of current

flow in terms of the direction of the poling field and also predicts that while

the total charge released is proportional to the temperature or "pressure change,

the current depends on the rate of pressure or temperature change and can be

quite large. This effect can be described mathematically as follows.

In terms of the material's relative permittivity k" the equilibrium fieldinduced polarization is given by,

P = (k' - 1) e Q

L (4.7)

where e is the permittivity of vacuum and E is the apulied field. In the

o molecularly mobile liquid phase the field produces a polarization

P L

(T) = (K

L

(T) - 1) c o Ep

(4.8)

where the subscript L refers to the liquid phase,(T) to the functional dependence

on temperature and E

p

= 0/s is the nominal poling field. During poling, the field

maintains this polarization while the temperature is lowered enough to immobilize

the molecular dipoles. The field is removed and the lost polarization (neglecting

volume change) is,

P

c (T) = (k (T) - 1) e E (4.9)

s s or

where the subscript s refers to the solid phase.
- 7 -

Thus the frozen-in non--equilibriuin polarization remaining after removal of

the poling field is:

P (T) = (k (T ) O L L

K

g (T» e o E

p

(4.10)

where T is the temperature where the material becomes liquid. Eq. (4.10)

J_j provides a method of calculating the frozen dipole polarization for linear

dielectrics from a knowledge of their relative permittivity at the polar and

measuring temperatures. In order to calculate the piezoelectric and pyroelectric

coefficients from molecular properties one needs to use a more detailed model as

shown below.

The polarization (dipole moment per unit volume) is defined as

where N is the number of dipoles, V the volume of the electret and <m> the mean

effective dipole moment in the direction of P. As a model for the electret with

preferentially ordered polarizable dipoles of permanent moment u , consider Fig. 4.7

One can use an Onsager type calculation [4.26] to determine the effective moment

<m> in Eq. (4.11) of a representative dipole located in a spherical cavity and

oriented at a fixed average angle 6 with respect to the direction of overall

polarization P. Such a calculation leads to the result [4.27]:

where is the high frequency relative permittivity related to the polarizability

through the Clausius-Hosotti relationship and N/V is the number of dipoles per

unit volume. This important equation can be used to calculate the piezo- and

N <m>/V (4.11)

P = (k + 2) N u <cos G>/3V (4.12)
- 8

-

pyroelectric coefficients for this model. This calculation is done simply by

taking; the derivatives of P with respect to pressure and temperature and then

expressing the relationship between these derivatives and the defined quantities

(4.3) and (4.4).

The relationship between P

q of Eq. (4.12) and electric displacement is

given by

D=k'eE + P

o o (4.13)

In the simplest case where the short-circuit current is measured while temperature

or stress are changed, one obtains:

3D

3T

E=0,T

3P

c 3T

E=0,T

3 (Q/A)

3T (4.14)

E=0,T

and

3D

^

E=0,T

3P

c 3T

3(Q/A)

E=0,T

^

(4.15)

E=0,T

where Q/A is the surface charge per unit area of electrode. Here we continue to

neglect changes in (Q/A) due to real charges.

Generally it is not a change in (Q/A) which is measured but rather a change

in Q. Reported values for piezo- and pyroelectric coefficients are thus in

error as far as the strict definitions are concerned. In the following we adopt

common practice and redefine (4.3) and (4.4) as,

d = (1/A) (3Q/3T) E=0,T

(4.16)

and

p = (1/A) (3Q/3T) E=0jT

(4.17)
- 9 -

The above distinction becomes particularly significant for polymers where

the difference between (4.14) and (4.16) is of the order of magnitude of the

terms themselves. Inorganic materials have a much smaller temperature and

stress-induced area change and the corresponding difference between (4.14)

and (4.16) or (4.15) and (4.17) is small.

Another inconsistency is sometimes encountered when measurements are

reported at voltages considerably greater than zero. Allowing X to represent

stress or temperature, the derivative,

3D

~9X

8k

9X

9E 3P

_ e E + k's — + —

E o o 3X 8X E (4.18)

has two terms in addition to that in (4.14) and (4.15). The first term involving

electrostiction can be large if E is large. From (4.3) and (4.4) this is a

legitimate part of p and d which are functions of E. The second term would not

appear if E were held constant, but in practice it is the voltage $ that is held

constant and the thickness s = $/E varies with the measurement and gives an

electromechanical contribution. Similarly the third term is measured at constant

$. (Electrostriction and electromechanical contributions are considered in a

different way in Ref. [4.30]).

To reduce ambiguity, we will consider measurements made at zero field and

for simplicity and a more straight forward comparison of p and d, will use

hydrostatic pressure as mechanical stress (positive pressure is a negative stress)

Without giving the details, [4.27], the straight-forward differentiation of

Eq. (4.12) to obtain the pressure and temperature induced currents in an
- 10 -

electret gives:

A

_1

(8Q/9T)

p

= - P

q

a(K

m + c}> 2 /2aT + 3y4> 2

) (4.19)

A

_1

(9Q/3p)

T

= P

q BCk^ + 3Y 0 2

)

• (4.20)

where a = (3V) ^ dV/dT is the linear coefficient of expansion, 6 = ~(3V) ^ dV/dp

is the linear compressibility, y = Voi dw/dV, is a Gruneisen constant for the

2 dipole torsional frequency co and cf is the mean squared torsional displacement

of dipole fluctuations.

These equations show that for this model most of the piezo- and pyroelectric

response comes from volume expansion and its effect on k . There is an additional

contribution from temperature change which can be illustrated with a physical

model like that in Fig. 4.8. Although the dipoles have a fixed mean direction,

there is always thermal motion whose mean squared amplitude in the simple harmonic

approximation is proportional to temperature. Thus increasing the temperature of

a dipole reduces the average magnitude of its moment. This effect was the basis

of a theory of pyroelectricity in PVF due to ASLAKSEN [4.28], and accounts for

about 1/3 of the pyroelectricity in PVC and possibly a similar fraction in other

polymers. The amplitude of molecular librations is difficult to measure or to

predict d pfvtOKA. because of the large number of vibrational modes and molecular

conformations contributing. However, one recent paper gives a value of 10°

for the root mean squared torsional displacement of polyethylene molecules based

on x-ray data [4.29].

4.3 Symmetry and Tensor Components

Crystal symmetry is usually considered in discussions of piezoelectricity.

An isotropic amorphous material could not be expected to be either piezo- or

pyroelectric because its response to stress will be the same in all directions.
- 11 -

However, if one preferentially aligns molecular dipoles in the specimen, there

is an axis of symmetry in the direction of the net moment and the sample will

be both piezoelectric and pyroelectric . Often, polymer films are uniaxially

stretched to preferentially align the polymer molecules parallel to the

stretch direction and they are then poled to align the dipoles normal to both

the stretch direction and the plane of the film. (We consider only those

polymers with dipoles normal to the molecular axis). The result is to destroy

the axis of symmetry present in the unstretched specimen. The axes are usually

identified as shown in Fig. 4.9. The expected components of the piezoelectric

tensors for such a specimen and their proper signs are:

0 0 0 d+ 0

0 0 d+ 0 0 ) (4.21)

d+ d~ 0 0 0

32 j3

p =^0 j

(4.22)

The assignments can be made by inspection from Fig. 4.9. Stress in the

+ 3 direction will increase the sample thickness and thus decrease the polarization giving a negative d^. The stress in the 1 and 2 directions will decrease

the thickness and increase polarization, giving a positive d_. and d„_. Exoeri31 32

mentallv, d„ n is found to be negative for PVF_ [4.15] and d_- oositive for PVF

33 2 31

[4.31] and predominently positive for PVF„ [4.16]. d was also found to be

negative with hydrostatic stress for PVC [4.33]. (Remember that we are using

the assumption that the electrodes expand with the specimens and that we have

adopted equations (4.16) and (4.17) as our definitions. If we use the proper
12 -

definitions given by equations (4.14) and (4.15) stress in all three directions

1, 2, and 3, will increase the volume and decrease the polarization giving negative

d^. components). The shear components result because a positive shear about the

1 axis, T^, rotates the dipoles into the + 2 direction and a shear about the 2 axis,

T^, rotates the dipoles into the + 1 direction. Neither shear causes a

change to first order in the moment in the 3 direction. A shear about the

3 axis, T^, does not change the moment. Because there is no net moment

along the 1 and 2 axes, p^ = p£ = 0 and an increase in temperature produces

an increase in volume and decrease in polarization yielding a negative p^.

The ci matrix constructed from physical arguments for amorphous polymers is

characteristic of symmetry. This same symmetry is found for the polar

crystal phase of PVF^ [4.31] and the same crystal structure is reported for

polar PVF [4.32]. Poled, unoriented polymers should give d^^ = d^^ and

d_. = + d n

r

characteristics of a piezoelectric matrix with C _ _ symmetry

24 15 °°V

[Tlef. 4.5, Sect. IA]

.

4.4 Structure

4.4.1 General

Using the model discussed above it is possible to hypothesize three

requirements for piezo- and pyroelectricity in polymers. i) There must be

molecular dipoles present, the higher their moment and concentration the better.

ii) There must be some way of aligning the dipoles, the more alignment the better.

iii) There must be a way of locking- in the dipole alignment once it is achieved,

the more stable the better. Evaluating these conditions for a particular polymer

requires considerable data on the molecular and bulk structure and properties.

In the following discussion we consider in some detail two different types of

polymers—amorphous and semi-crystalline. Other types —notably the biopolymers

will not be considered.
- 13 -

The polymers we will be discussing consist of a saturated carbon backbone

Xi7ith various combinations of fluorine, chlorine and hydrogen. The abbreviations

to be used for the repeating monomer units are defined in Table 4.1 which refers

to Fig. 4.10. A repeat unit consists of two carbon atoms and conformations are

allowed by rotations of 2tt/ 3 rad. about carbon-carbon bonds.

4.4.2 Amorphous Polymers

PVC is an example of an amorphous polymer which can be made piezo- and

pyroelectric [4.6, 33-35]. The repeat unit is polar with an effective dipole

-30

moment of 3.6 x 10 C*m (1.1 D) [4.36]. The usual form of PVC is amorphous

because of the irregular positioning of CI between sites 3 and 4 (Fig. 4.10).

More stereo-regular (syndiotactic) crystallizable PVC can be made and its crystal

structure has been determined [4.3 7]. PVC is an equilibrium liquid above its

glass transition temperature (about 80°C) although thermal decomposition is

appreciable above this temperature. Below 80°C, the kinetics of molecular

reorganization are slow enough that a non-equilibrium amorphous solid (glass)

is formed. Structural relaxation times of the glass increase rapidly with

decreasing temperatures to the order of years at room temperature. Thus this

polymer fits all criteria in 4.4.1 for piezo- and pyroelectricity . To illustrate

the calculation of p and d we rewrite (4.19) and (4.20) to account for the fact

that the dipoles are small enough that the product of their moment times the

field is much less than their thermal energy kT and (4.10) will be valid. For

more background see [Ref. 4.38, p. 32].

(4.23)

d = - Ak'e E 3 [k + 3y<T] (4.24)

o p
- 14 -

We use Ak' = 10 and = 3 [4.36], a = 0.78 x 10~ 4

/K, 6 = 0.86 x 10

_1

°m

2 /N

2 [4.33], T = 300 K and <\> =0.07 rad. (from estimate of <f> = 15°). The Gruneisen

constant is expected to be small because the force constants for dipole rotation

are mostly intramolecular and do not depend strongly on volume. Neglecting the

2 terms in y, we find p = -0.10 nC/cm . K and d = -0.73 pC/N when = 320 kV/cm,

in good agreement with measured values [4.39].

Even if one does not have dielectric data, the quantity Ak' can be calculated

with reasonable confidence from the dipole moment using Onsager's equation [4.36].

REDDISH [4.36] interpreted the dielectric data on PVC as indicating that the

length of the relaxing segments increased as the temperature decreased below T

and since the Aic" increases linearly with the number of dipoles per rigid unit,

large polarizations could be achieved. Unfortunately, we found no enhancement

of p and d by lower temperature poling of PVC and suspect the observed effects

in dielectric properties are due to space charge.

Since most of the variables in (4.23) and (4.24) will be similar for all

polymer glasses, larger coefficients can be. sought from polymers with a large

dipole moment (p and d will increase as the square of the dipole moment per

unit volume) and by increasing the poling field. A possible candidate is PAN

with a dipole moment greater than 4D. Unfortunately PAN may have an anomalous

liquid phase in which dipole-dipole forces prevent normal polarization [4.40]

contrary to criteria (ii) in Subsect. 4.4.1. In other cases the dipoles may

not become immobile at T (e.g. polymethylmethacrylate) contrary to criteria

(iii)). A thermally stable, high T polar glass may have useful high temperature

applications, but presently the most sensitive piezo- and pyroelectric polymers

are semicrystalline

.
- 15 -

4.4.3 Semicrystalline Polymers

The most interesting of the semicrystalline polymers are PVF2 and PVF.

These polymers crystallize because the fluorines, unlike the large chlorines,

are close enough in size to hydrogen so as not to interfere with regular packing.

Both polymers have head-head and tail-tail defects, where successive repeat

units are backwards. These amount to 5% for PVF

2 [4.41-43] and 25-32% for PVF

[4.41]. A h-h unit in VVF^ is immediately followed by a t-t unit [4.41] so

that 5% of these defects cancel 10% of the dipole moment of the planar zig-zag

chain. The dipole moment of a PVF^ repeat unit can be estimated from the

-30

average of those for dif luoroethane and dif luoromethane [4.44] at 7.06 x 10 cm

(2.12D). The moment for PVF in the plane of the trans planar C-C zig-zag will

be very close to 1/2 that of PV^' ^ ut ^"^ defects will reduce the net

moment of the planar PVF molecule by 60%. Both of these polymers have good

thermal and chemical stability.

Semicrystalline polymers consist of lamellar crystals mixed with amorphous

regions. A schematic diagram of a semicrystalline polymer is shown in Fig. 4.11

for a low and high density sample. Annealing or crystallizing for longer times,

at higher temperatures and pressures increases the lamellar thickness and

perfection which results in a higher sample density. The crystals grow in the

form of spherulites and studies on the morphology of PVF^ show that three crystal

phases have distinct morphology and can grow simultaneously from the melt or one

phase can grow at the expense of another [4.45]. A typical molecular weight

5 _ g for these polymers is 10 for an extended length of 50 x 10 m and a total of

—8

2000 repeat units. Since the lamellae are of the order of 10 m thick, a single
- 16 -

molecule folds back and forth through the lamellae many times. When stretched

to several times the original length, the specimen becomes oriented such that

the lamellae are normal to the stretch direction and the molecules are parallel

to the stretch direction [4.46-47]. PVF and PVF

? are of the order of 50%

crystalline.

The dispersed amorphous phase seems to have normal equilibrium liquid

properties with a liquid-glass transition region around -50°C, and a WLF-type

dielectric relaxational behavior [4.17, 48, 49]. Broad line NMR [4.48, 50],

and mechanical relaxation data [4.5, 31, 42, 50, 51] also show a normal liquidglass relaxation. The magnitude of the dielectric dispersion and room temperature

relative permittivity increase with amorphous content as expected [4.49, 50].

From criteria (iii) in Subsect. 4.4.1 we do not expect the amorphous phase to

contribute to piezo- and pyroelectricity . MURAYAMA [4.8] has stated the same

conclusion.

Three crystal phases have been reported for • Form 8 and y (alternatively

forms I and III) are similar in that the molecules assume a planar zig-zag conformation and pack in the crystal with dipole moments parallel. The a form

(Form II) is in a trans-gauche-trans-gauche ' conformation which is a polar

molecular configuration but which packs to form an antipolar crystal. Projections

of the a and the 3 and y crystals onto a plane normal to the molecular axes are

shown in Fig. 4.12, [4.52]. The crystal structure of PVF is the same as 3 phase

PVF2 [4.32]. Vibrational analyses of the proposed structures [4 . 52 , 53] have been

done to make detailed assignments of the spectral absorptions in PVF2. Crystal

melting points range from 230°C for PVF [4.54] to around 190°C for PVF y phase,
- 17 -

180°C for PVF

2

6 phase and 170°C for PVF

2 a phase [4.45]. Crystallization

from the melt at lower temperatures produces a phase and at higher temperatures

Y phase [4.45, 55]. The B comes from stretching or rolling a or y phase material

[4.52]. The y phase can also be cast from certain solvents [4.52]. Mixtures

and copolymers of PVF and PVT^ tend to stabilize the polar crystal form [4.54].

Model calculations of the effects of VF^, VF, and TFE repeat units copolymerized

with PVF^ indicate the 6 phase becomes stable above a 5-10% concentration of

these substituents [4.56] which has also been shown experimentally [4.57]. Work

in our laboratory has been done on a copolymer of 73% VF^ and 27% TFE [4.58] which

is completely $ phase in accord with the above prediction [4.56]. Copolymers of

VF2, VF and TFE can be highly piezo- and pyroelectric [4.9].

The usual methods of identifying the fraction of crystallinity in a specimen

are to compare its density to the crystal and amorphous densities [4.59] or to

compare its heat of fusion to the crystalline heat of fusion [4.45]. The usual

measures of crystal phase fractions are x-ray diffraction [4.60] and infra-red

absorption [4.55] intensity ratios.

4 . 5 Properties of Semicrystalline Polymers

4.5.1 Crystal Relaxations

In the crystal phases of PVF and PVF

2 the question of rotational freedom

of the dipoles is critical [Subsect. 4.4.1, ii]. Ample dielectric relaxation

data exist on PVF [4.61] and a phase PVF

2 [4.17, 49, 59, 61-64] and mechanical

data on PVF [4.51] and a phase PVF

2 [4.50] and thermally stimulated current (TSC) data

on a phase PVF

2 [4.17] to conclude that a crystal relaxation occurs at about

80°C at a measuring frequency of 100 Hz. At room temperature the relaxation

time x of the a relaxation is increased to about 1 sec. Log t is linear with

c c c
- 18 -

1/T and the activation energy is around 100 kJ/mol. The 3 phase of PVF^ is

reported to have a mechanical crystal relaxation at 110°C at 10 Hz [4.31, 50].

Its activation energy has not been determined. A dielectric a^ relaxation

in 3 and y phase PVF^ have yet to be clearly observed, but may be masked by

rapidly increasing and k" with temperature. This behavior is usually

attributed to space charge effects [4.61, 63, 64]. TSC data give strong background currents even from unpoled specimens [4.11]. At lower temperatures current

2 with a broad maximum at 80° and integrated charge of up to 3 uC/cm is observed

[4.20]. It is useful to infer the behavior of the a relaxation in 3 and y PVF.

c 2

from that in a phase PVF~, PVF and PE. That the dielectric a is a crystal

2 c relaxation was shown for a phase PVF£ by the dependence of its amplitude on

crystallinity and by observing its disappearance at the melting temperature [4.49].

That it can exist in the 3 phase is demonstrated by its presence in PVF [4.61].

That it probably involves rotation of an entire intralamellar segment with twisting

at the lamellae surfaces is likely considering that this is the well documented

mechanism in PE [4.65]. Since twisting must be about C-C bonds, these

rotations would be restricted by the crystal fields of neighboring molecules.

This model is also consistent with the dependence of the a relaxation parameters

on molecular thickness [4.48, 59, 63]. The magnitude of the relaxation can be

calculated from the two site model (sites 180° apart) [4.65].

c

(4.25)

where f is the fraction of dipoles in the ordered site. If U is the energy

difference between sites, f = exp (-U/kT) / [1 + exp(-U/kT)] and

f(l - f) = exp (-U/kT) /[I + exp (-U/kT)]

2

. (4.2 6 ]
- 19 -

Since we are measuring a composite of amorphous and crystalline regions

we must also use an equation like that for concentrated, nonconducting dispersions [4.66, 67].

:< x 1/3

0c

£ /o = 1 - if (4.27)

- KX

In the above equations, <

g and <^ are the relaxed and unrelaxed relative permittivities for the crystal, [Ak^ = k - < ], N and u are the number ner unit volume

x s

00 r

and the dipole moment of the relaxing units, k, and <. are the relative permittivities of the sample, crystal and liquid respectively and o is the volume fraction

of crystals in the sample. Equation (4.27) should be replaced by a more general

equation for conducting dispersions [4.68] when necessary. Note from (4.27) that

the amplitude of the crystal and liquid relaxations as measured will be considerably smaller than if measured in each phase separately.

It is instructive to consider 3 phase PVF where we assume a rigid chain of

40 repeat units in the lamellae. 60% of these are nonpolar because of head to

—28

head defects and their effective rigid-rod moment will be 16 x 3.3 x 10 Ocm.

22 -3

The number per unit volume is 1.8 x 10 /40 cm , and T = 350 K. The relaxation

amplitude is from <

' = 3 to 13 [4.61] (remembering Eq. (4.27)). For these

conditions, one finds that the fraction of disordered molecules is 8% and

U/kT = 2.6. These are quite reasonable values for a crystal with such disordered

molecules (30% head to head defects). Now consider U/kT for PVF^ in the same

6 phase. It will have twice the dipnle moment per repeat unit and, with 5%

head to head units, 9/4 the number of dipoles for a 40 unit rigid chain. Suppose

the energy between the ordered and disordered sites is proportional to the

x
- 20 -

net difference in the number of fluorines in the sites. Like the dipole moment,

the number of fluorines rotated will be 4 1/2 times as great for PVF2 as for PVF.

This gives a value of U/kT of 12 and a disordered fraction of only 10 . The a

c —5 9 — relaxation amplitude for 3 phase PVF

2 then is only (10 /0. 08) (4.5) =10 that

of PVF which would not be observable with ordinary dielectric measurements.

4.5.2 Ferroelectricity

PVF2 in the polar form is often supposed to be a ferroelectric [4.69, 70],

which means that it not only is a polar crystal but that the polarity is switchable

with an electric field. Direct evidence for a field induced change in the unit

cell orientation in PVT^ measured by x-ray pole figures has been reported [4.21].

Molecular orientation measurements using Raman techniques suffer from the dilution

effect of the liquid phase [4.71]. The usual hysteresis measurements of charge

vs. field are difficult because of space charge effects and the results are

ambiguous. Measurement of piezoelectric [4.11, 30] and pyroelectric [4.72]

response as the field is cycled from large positive to negative values does give

a hysteresis loop. A poled PVF£ film was shown to require 450 kV/cm to suppress

its piezoelectric response [4.30]. High dielectric constants of the order of

1000 [4.72] are also indicative of ferroelectric switching in 8 phase PVF 2 but

since the same behavior occurs in non-polar a phase PVF^ as well [4.64], space

charge effects are probably dominant.

Polarization vs. time measurements for PVF^ show two relaxations according

to some authors. MURAYAMA et. al . [4.9] report a fast response at less than a

second and a slow response at 1-2 hours. FUKADA and OSHIKI [4.73] report the

fast response at 1 minute and the slow response at 1 hour. In measurements of

pyroelectric response the uniformity of polarization increased significantly when

the poling time was increased from 5 to 30 minutes [4.18].
- 21 -

There is disagreement about whether polarization saturates at high

temperatures and high fields. MURAYA31A et. al [4.8, 9] reported no saturation

for the piezoelectric response in ?VF

? and DAY et. al [4.18] report none for

the pyroelectric response (although the data for only uniformly poled samples

do show saturation effects) [4.18]. Other data [4.31] shows saturation of the

piezoelectric response in PVF2 arK* i- n our laboratory both the piezoelectric and

pyroelectric response of VF--TFE copolymers saturated as functions of field

and temperature [4.39].

Returning again to the calculations of Subsect. 4.5.1, the rigid PVF chain

-28

with a moment of 16 x 3.3 x 10 Ocm when subject to an internal field of

10^ V/ cm (about 4 times the applied field (4.25)) applied in a direction opposite

to the crystal moment will reduce the energy difference between the ordered and

disordered sites by 2 uE/kT to U /kT = 0.6. Thus in a time of the order of

-1 -3

the relaxation time t = (2ir x 100 Hz) = 10 sec at 80°C [4.61] a fraction,

f = 1/3, of the dipoles will reorient to the disordered site thus reducing the

energy difference between the sites by 2/3 and making the formerly disordered

site the new ordered site. For PVF_ from the same example U/kT is lowered by

2 uE/kT from 12 to U_/kT = 3 so that 5% of the chains would be switched by the

E

field. If this switching lowers 0 (mean field approximation) by 5% to 11.4, then

U^/kT = 2.4 and another 4% will switch lowering U^/kT further until all molecules

E E

switch. In a drawn specimen the molecular axis will be in the plane of the film.

Those dipoles which are at 90° to the poling field will not experience as great

an energy advantage as a result of switching and perfect- alignment is not expected

This situation is similar to that for 3aTi0

? where it is shown that a semicrystall

sample achieves only about 1/3 the polarization of the single crystal [Ref. 4.22
- 22 -

p. 218]. Both the data and a high field extension of simple dielectric theory

support the suggestion that PVF and the g form of PVF

2 are ferroelectric.

4.5.4 Space Charges

Space charge measurements are frequently made by measuring the currents

generated by heating, at a uniform rate, a specimen with evaporated electrodes

which has previously been cooled under an applied field. The thermally-stimulated

short-circuit currents (TSC) result from dipole reorientation and from the

change in the dipole moment of the space charge distribution [4.74]. Studies

on both amorphous and semicrystalline polymers have shown the space charge to

be predominantly positive near the negative poling electrode and negative near

the positive poling electrode (heterocharged electret) . Kerr effect measurements

in liquid nitrobenzene with dc fields show uniform space charge distributions

—8 3 with a net positive charge density of the order of 10 C/cm [4.75]. (For a

further discussion of such inconsistencies, see Subsect . 1.7.3). Dielectric

measurements of PVF and PVF^ typically show anomalously high values of k" at

high temperatures and low frequencies [4.61, 64, 76]. This effect is generally

attributed to ionic space charges [4.64]. It was shown that the interfacial

polarization in solid PVF^ is different from the electrode interfacial polarization

effects in liquid PVF 0 and was attributed to space charge polarization at the

liquid-crystal interfaces [4.64]. In TSC measurements it was shown that repeated

cycling of PV^ from 25 to 100°C with an applied field, reduced the space charge

effects [4.17]. Space charge concentrations in liquid nitrobenzene [4.75], and

the space charge effects seen in dielectric measurements of PVF^ [4.61, 64, 76]

and PVF [4.61] were also reduced by application of dc fields for several hours.

This reduction partially recovers with time after removal of the field

[4.61, 64, 76].
23 -

The general behavior of a conducting liquid with dispersed crystals of

roughly equal volume is quite complicated [4.68]. If, as seems likely, ferroelectric switching of the polar cyrstals occurs during the early stages of

poling then continued poling results in a flow of charge, mostly through

the more conductive liquid phase regions with positive charges moving toward

the negative electrode and negative charges toward the positive electrode.

At normal poling temperatures (~ 100°C) the current is time dependent and bulk

interfacial polarization effects are evident [4.64]. The charge carriers should

tend to pile-up at the crystal surfaces where their normal drift is hindered,

as shown in Fig. 4.13. This situation is analogous to concentrated emulsions

of oil and water [4.67]. TSC results show that space charges are released

at temperatures higher than the dipole relaxation maxima and these for PVF^

are considerably above room temperature [4.74, 77]. As a result, when the

specimen is cooled to room temperature the charges are immobilized and remain

at the crystal surfaces as in Fig. 4.13. The space charges form a dipole which

has the stiffness of the crystal and will produce a piezo and pyroelectric

response [see Subsect. 4.2.2]. Note however that the space-charge dipoles if

formed from interfacial polarization of the poling-current charges are opposing

the molecular dipoles and will reduce the piezo- and pyroelectric response. It

is difficult to predict the magnitude of this effect but it will be bigger, the

higher the space charge concentration or equivalently the higher the poling

current. The observation of a slow poling process reported for PVF^ [4.9, 30],

whereby the piezoelectricity slowly increases with time, and the observation

that space charges are removed by dc fields on a similar time scale [4.17, 61,

64, 75, 76], support the idea that a decrease in space charge reduces the masking
- 24 -

effects of space-charge dipoles. Also the partial decay of piezoelectricity

with time after removal of the field [4.9] and the partial recovery of space

charge density with time [4.61, 76] may be similarly related to the postulated

space-charge dipoles.

4.6 Measurements and Data

Piezo- and pyroelectric measurements on polymer films are usually made

by applying tension to a strip of polymer and measuring on opposing electrodes

the short-circuit charge or open circuit voltage due to a change in the tension.

The stress and strain are measured with a load cell and strain gauge and the

stress is usually sinusoidal. This basic technique has been discussed previously

[4.5, 7], Measurements can be made by clamping a sample in a vise in series

with a load cell. Noise can be reduced for these measurements by the use of good contact

electrodes (e.g. evaporated). A double film sandwich with the high potential

electrodes together and shielded by the outer grounded electrodes greatly reduces

noise problems. Piezoelectric measurements have also been made by applying a

field to the specimen and observing the length and thickness changes [4.16],

by analyzing the response of a piezoelectric film driven electrically in the

neighborhood of its resonant frequencies [4.12] and by applying hydrostatic

pressure to the film with He gas [4.33]. Pyroelectric measurements are conveniently made by changing the temperature of the specimen and measuring the

charge produced [4.33]. Heating and cooling can be done with a Peltier device

[4.78] which is noiser than a heater or, for electromagnetic purposes, with

optical radiation [4.19]. The accuracy of piezoelectric data is hard to assess

since error analyses are seldom mentioned. Piezoelectric and electrostriction
- 25 -

data on PVF^ as a function of temperature and frequency has been adequately

reviewed previously [4.5, 7, 9].

Applications for polymer transducers or reflectivity measurements [4.79],

a photocopy process [4.14], radiation detectors [4.19], night vision targets

[4.80], intrusion and fire detectors [4.81], hydrophones [4.82], earphones

and speakers [4.10], pressure sensors, strain gauges and many more are being

developed or investigated.

4.7 Dipole Model Applied to Semicrystalline Polymers

Eqs. (4.19) and (4.20) can be applied to single crystals of 3 phase PVF^

.

2 The moment of the crystal will be 13 uC/cm which gives a polarization of 13 •

2 (k + 2)/3 a 22 pC/cm . The linear coefficient of expansion (based on copolymer

data) [4.39] and the linear compressibility [4.39] in the polarization direction

are about 2 x 10

4

/°C and 2 x 10 ^m^/N. The molecular moment of inertia about

the center of mass is I = 0.7 x 10 Kgm and the torsional frequency u

q

/2tt =

12 2 1^2 o 2.1 x 10 /sec [4.52]. The harmonic approximation gives <j>° = (kT/lu^) ' =11.4°

at room temperature for the rigid rod. Higher order torsional modes will reduce

this amplitude so we will assume the polyethylene value [4.29], CD = 10°. Thus,

very roughly, for the single crystal (sx)

,

p (sx) = 22 • 10~ 6 C/cm2

• 2 • 10~ 4

K

_1

[3 + 0.03(2 • 2 10~ 4

K

_1

- 350 K)" 1

„ (4.28) + 3 • 2 • 0.17] = 16 nC/cm .K

d (sx) = 140 pC/N (4.29)
- 26 -

The coefficient d., results from the thickness change in the 3 direction

31

due to a stress in the 1 direction,

d (sx) = p n 31

[e^ + 6y4> 2 ]/Y

1 = 120 pC/N (4.30)

9 2 where n^-^ ~ is the assumed Poisson's ratio and Y^ = 2 x 10'N/m is Young's

modulus [4.31].

Ferroelectric ceramic powders in an amorphous polymer matrix were measured

[4.83] but not enough details are available to help with the present prediction.

The dipole model (Fig. 4.7) can be extended by assuming the Onsager cavity

represents an entire crystallite but other assumptions (e.g. no space charges

and the sum of the cavity volumes equals the specimen volume) are clearly not

valid for the semicrystalline case. However, using the same factor 1/3 for

dipole switching efficiency as for BaTiO^ [4.22] and 1/2 for the crystal fraction

of the specimen, one gets the results in Table II.

These numbers are close to the highest observed values for drawn polar

phase PVF^. To illustrate further application of the model we return to the

calculations of Subsect. 4.5.1 where it was shown that the polarization of WY^

is 4 1/2 times that of PVF. Eqs. (4.23) and (4.24) predict that p and d will

also be 4 1/2 times greater for PVF£ than PVF. The highest reported p's for

2 2 these two polymers are 4.1 nC/K-cm [4.19] and 1 nC/K-cm [4.86] respectively.

The ranges of d^'s reported by KAWAI [4.6] for PVF and PVF are 3-7 pC/N and

1-1.3 pC/N respectively.

The model also predicts that the piezoelectric stress constant e = n Pte^ -1- 6ycf>] will vary with orientation and temperature only because of variation

in Poisson's ratio n . It is known that e is a strong function of both temperature
- 27 -

and orientation [4.7] beyond the usual variations in n (1/3 to 1/2). These

limits do not hold for anisotropic materials such as drawn semicrystalline

polymers and direct measurement of n has yet to be made. The predicted ratio

of the reduced temperature-induced-strain response p/a to the reduced pressureinduced-strain response d/S is 1.1. This differs significantly from the ratio

of 2 typically measured in our laboratory, and is the most serious disagreement

with experiment we have yet discovered.

Other models for piezoelectricity in PVT^ include orientation of dipoles

in an anomalous liquid phase [4.87] and increased perfection of the planar

zig-zag structures [4.12] both by applied stress. These models are strongly

supported by the observation that a strain in the direction of the molecular

axes gives a much bigger response than a strain perpendicular to the axes,

z 5 d^2 [4.7]. Calculations on the polarization kinetics using several

models for PvT^ have been made [4.88].

4.8 Summary and Conclusions

Some polymers can be made both piezo- and pyroelectric by cooling them

in the presence of an applied field. This effect is true piezo- and pyroelectricity rather than electrostriction, conduction, electromechanical effects

or the motion of conductors in the field of space charges. Two distinct types

of polymers can be piezoelectric. Amorphous polymers are piezo- and pyroelectric

by virtue of a non-equilibrium but kinetically stable net dipole orientation.

The semicrystalline polymers are piezoelectric due to alignment of polar,

ferroelectric crystals dispersed in the amorphous phase. In both types the

magnitudes of the piezo- and pyroelectric effects are in accord with the
- 28 -

expected temperature and pressure dependence of the dipolar polarization,

i Space charges embedded in the polymer normally will not produce a piezo- or

pyroelectric current. Those embedded near the crystal-liquid interfaces tend

to reduce the piezo- and pyroelectricity . Improved orientation of dipoles and

reduction of ionic impurities should increase p and d for PVF2 by a factor of

three above typical values presently reported. The sensitivity of amorphous

polymers is limited mainly by dipole moment per unit volume and breakdown

strength.

The model presented here was developed along with the writing and was used

as a framework for the presentation in order to make the chapter more interesting

to the authors and hopefully also for the readers. It is hoped that the model,

still largely untested, will provide direction and stimulation for further

work in this field.

\cknowledgement

Partial suoport of this work by the Office of "aval Research is

gratefullv acknowledged.
- 29 -

References

4.1 Heaviside, Electrical Papers, Macmillan, London 1, 488 (1892, or Electrical Papers, I. Macmillan, London (1892) p. 488.

4.2 M. Eguchi, Phil. Mag. 49, 178 (1925).

4.3 E. P. Adams, J. Franklin Inst., 204, 469 (1927).

4.4 A. Meissner and R. Bechmann, Z. tech Phys. 9_, 174, and 430 (1928).

4.5 E. Fukada, Progress in Polymer Science, Japan _2, 329 (1971).

4.6 H. Kawai, Jap. J. Appl. Phys. 8, 975 (1969).

4.7 R. Hayakawa and Y. Wada, Advances in Polymer Science, Springer-Verlag,

11, 1, (1973).

4.8 N. Murayama, J. Polym. Sci., Polym. Phys. Ed., 13, 929 (1975).

4.9 N. Murayama, J. Polym. Sci., Polym. Phys. Ed., 13, 1033 (1975).

4.10 N. Tamura, T. Yamogughi, T. Ayaba and T. Yoshimi, Pioneer Electronic

Corp., Reprint No. 986 (G-4) Audio Engineering Society, N.Y. 49th

Convention (1974).

4.11 M. Tamura, K. Ogasawara, N. Ono and S. Hagiwara, J. Appl. Phys., 45 , 3768 (1974).

4.12 H. Ohigashi, submitted to J. Appl. Phys.

4.13 J. H. McFee, J. G. Bergman, Jr., and G. R. Crane, Ferroelectrics , _3, 305 (1972).

4.14 J. G. Bergman, G. R. Crane, A. A. Ballman and H. M. 0' Bryant, Jr.,

Appl. Phys. Lett., 21, 497 (1972).

4.15 G. Pfister, M. Abkowitz and R. G. Crystal, J. Appl. Phys. 44, 2064 (1973)

4.16 H. Burkard and G. Pfister, J. Appl. Phys. 45, 3360 (1974).

4.17 M. Abkowitz and G. Pfister, J. Appl. Phys. 46, 2559 (1975).

4.18 G. W. Day, C. A. Hamilton, R. L. Peterson, R. J. Phelan, Jr. and L. 0.

Mullen, Appl. Phys. Lett. 24, 456 (1974).

4.19 R. L. Peterson, G. W. Day, P. II: Gruzensky and R. J. Phelan, Jr., J. Appl

Phys. 45, 3296 (1974).

4.20 R. G. Kepler and P. M. Beeson, Bulletin APS, Series II, 19 265 (1974)
- 30 -

4.21 R. G. Kepler, E. J. Graeber and P. M. Beeson, Bulletin APS Series II,

20, 350 (1975).

4.22 D. A. Berlincourt, D. R. Curran and H. Jafee, Physical Acoustics , Academic Press 1A, 183 (1964).

4.23 T. Furukawa and E. Fukada, Rep. Progs. Polym. Phys. Japan, 1(5 457 (1973).

4.24 R. E. Collins, Proceedings of the IEEE, 34, 381 (1973).

4.25 G. M. Sessler and J. E. West, J. Acoust. Soc. Am., 5_3, 1589 (1973).

4.26 L. Onsager, J. Amer. Chem. Soc, _58, 1486 (1936).

4.27 F. I. Mopsik and M. G. Broadhurst, J. Appl. Phys

4.28 E. W. Aslaksen, J. Chem. Phys. 5_7, 2358 (1972).

4.29 K. Iohura, K. Imade and M. Takayanagi, Polym. J. _3> 357 (1972).

4.30 M. Oshiki and E. Fukada, J. Matls. Sci. 10, 1, (1975).

4.31 E. Fukada and T. Sakurai, Polym. J. 2, 657 (1971).

4.32 R. C. Golike, J. Polym. Sci. 42, 582 (1960).

4.33 M. G. Broadhurst, C. G. Malmberg, F. I. Mopsik, and W. P. Harris in

Electrets, Charge Storage and Transport in Dielectrics , M. M. Perlman, Ed.

The Electrochemical Soc, N.Y. (1973).

4.34 J. Cohen and S. Edelman, J. Appl. Phys. 42, 3072 (1971).

4.35 M. G. Broadhurst, W. P. Harris, F. I. Mopsik and C. G. Malmberg, Polym.

Reprints (American Chemical Soc), 1_4, 820 (1973).

4.36 W. Reddish, J. Polym. Sci., Part C, No. 14, 123 (1966).

4.37 C. E. Wilkes, V. L. Folt and S. Krimm, Macromolecules , 6, 235 (1973).

4.38 A. von Hippie, Dielectric Matls. and Applications (Technology Press of

MIT and John Wiley and Sons, N.Y. 1954).

4.39 G. T. Davis, Special Issue of Anais da Academia Brasileira de Ciencias.

4.40 H. G. Olf, Research Triangle Institute, private communication.
- 31 -

4.41 C. W. Wilson, III, and E. R. Santes, Jr., J. Polym. Sci., Pt.C, _8, 97 (1965).

4.42 Von M. Gorlitz, R. Minke, W. Trautvetter and G. Weisgerber,

Die Angewandte Makromolekulare Chemie 29/30, 137 (1973).

4.43 J. P. Stallings and S. G. Howell, Polymer Eng. & Sci., 11, 507 (1971).

4.44 R. D. Nelson, Jr., D. R. Lide, Jr., and A. A. Maryott, Selected Values

of Electric Dipole Moments for Molecules in the Gas Phase , (NSRDS-NBS 10;

U.S. Government Printing Office, Washington, D.C.) 1967.

4.45 W. H. Prest, Jr. and D. J. Luca, J. Appl. Phys.

4.46 R. J. Shuford, A. F. Wilde, J. J. Ricca and G. R. Thomas, Nat . 3ur . Stand.

(U.S.) Interagency Rep. 75-760, pg. 59-96 (1975).

4.47 J. B. Lando, H. G. Olf and A. Peterlin, J. Polym. Sci.-Al, 4, 941 (1966).

4.48 N. Sasabe, S. Saito, M. Asahina, and H. Kakutani, J. Polym. Sci. A-2,

I, 1405 (1969).

4.49 S. Osaki and Y. Ishida, J. Polym. Sci., Polym. Phys. Ed., 12, 1727 (1974).

4.50 H. Kakutani, J. Polym. Sci. A-2, _8, 1177 (1970).

4.51 E. Fukada and K. Nishiyama, Japanese J. Appl. Pays., 11, 36 (1972).

4.52 M. Kobayashi, K. Tashiro and H. Tadokoro, Macromolecules , _8, 158 (1975).

4.53 F. J. Boerio and J. L. Koenig, J. Polym. Sci. A-2, 1_, 1489 (1969).

4.54 G. Natta, G. Allegra, I. W. Bassi, D. Sianese, G. Copoucci, and E. Torti,

J. Polym. Sci. Pt.A, 3, 4263 (1965).

4.55 S. Osaki and Y. Ishida, J. Polym. Sci., Polym. Phys. Ed., 13, 1083 (1975).

4.56 B. L. Farmer, A. J. Hopfinger, and J. B. Lando, J. Appl. Phys., _43, 4293 (1972).

4.57 J. B. Lando and W. W. Doll, J. Macromol. Sci., Phys., B2_, 205 (1968).

4.58 Kynar 7200, Pennwalt Corp.

4.59 K. Nakagawa and Y. Ishida, J. Polym. Sci., A-2, 11, 1503 (1973).

4.60 L. E. Alexander, X-ray Diffraction Methods in Polymer Science , John Wiley,

N.Y. (1969).
- 32 -

4.61 S. Osaki, S. Uemura and Y. Ishida, J. Polym. Sci. A-2, 9_, 585 (1971).

4.62 A. Peterlin and J. Elwell, J. Matls. Sci., 2, 1 (1967).

4.63 S. Yano, J. Polym. Sci., A-2, 8, 1057 (1970).

4.64 S. Yano, K. Tadano, K. Aoki and N. Koizumi, J. Polym. Sci., Polymer

Phys. Ed., 12, 1875 (1974).

4.65 J. D. Hoffman, G. Williams, and E. Passaglia, J. Polym. Sci., Pt.C,

No. 14, 173 (1966).

4.66 D. A. G. Bruggeman, Ann. Physik, _24, 636 (1935).

4.67 T. Hanai, N. Koizumi, T. Saigano and R. Gotoh, Kolloid-Zeitschrif t

,

171 , 20 (1960).

4.68 T. Hanai, Kolloid-Zeitschrif t , 171 , 23, (1960).

4.69 K. Nakamura and Y. Wada, J. Polym. Sci., A-2, 9_, 161 (1971).

4.70 J. H. McFee, J. G. Bergman, Jr. and G. R. Crane, Ferroelectrics , _3, 305 (1972).

4.71 G. L. Cessac and J. G. Curro, J. Polym. Sci., Polym Phys. Ed., 12,

695 (1974).

4.72 P. Buchman, Ferroelectrics, J5, 39 (1973).

4.73 E. Fukada and M. Oshiki , Nat. Bur. Stand. (U.S.) Interagency Rep. 75-760,

pg. 8-34 (1975).

4.74 J. van Turnhout , Polym. J., 2, 173 (1971).

4.75 E. C. Cassidy, R. E. Hebner, Jr., M. Zahn and R. J. Sojka, IEEE Trans,

on Elec. Insulation, 9_, 43 (1974).

4.76 S. Uemura, J. Polym. Sci., Polym. Phys. Ed., 10, 2155 (1972).

4.77 J. van Turnhout, Thesis Leiden (1972), TNO Central Laboratoruim Communication, No. 471.

4.78 A. W. Stephens, A. W. Levine, J. Fech, Jr., T. J. Zrebiec, A. V. Cafiero,

and A. M. Garofalo, Thin Solid Films, 24, 362 (1974).

4.79 W. R. Blevin and J. Geist, Appl. Opt., 13, 2212 (1974).

4.80 L. E. Garn and E. J. Sharp, IEEE Trans, in Parts, Hybrids and Packaging,

PHP 10 , 28 (1974).
- 33 -

4.81 J. Stern and S. Edelman, U.S. Natl. Bur. Stds. Technical News Bulletin,

56, No. 3, 52 (1972).

4.82 James M. Powers, Nat. Bur. Stand. (U.S.) Interagency Rep. 75-760,

pg.209 (1975).

4.83 E. Fukada and M. Data, Polym. J., 1, 410 (1970).

4.84 Kureha KF Piezo Element. Measured in our laboratory on sample supplied

by N. Murayama.

4.85 Kureha KF Piezo Element. Data supplied by N. Murayama.

4.86 R. J. Phelan, Jr. R. J. Mahler and A. R. Coole, Appl. Phys. Lett.,

19, 337 (1971).

4.87 R. Hayakawa, J. Kusuhara, K. Hattori and Y. Wada, Repts. Progr. Polym.

Phys. Japan, 16, 477 (1973).

4.88 R. E. Solomon and M. M. Labes, Natl. Bur. Stand. (U.S) Interagency Rep.

75-760, pg. 199-209 (1975)

.

USCOMM-NBS-DC

Table 4.1 Polymer identification for Fig. 4.10 according

to the hydrogen (H) fluorine (F) or chlorine (CI)

substituents in sites 1 thru 4.

Substituent

Polymer Hydrogen Fluorine Chlorine

Polyethylene (PE)

Polyvinylfluoride (PVF)

Polyvinylidenef luoride (PVF 2 ) Polytetrafluoroethylene (PTFE)

Polyvinylchloride (PVC)

Polyvinylidenechloride (PVD2)

Polychlorotrifluoroethylene (PCTFE)

Polyacrylonitrile (PAN)

1,2,3,4

1,2,3 4

1, 2 3,4

1,2,3,4

1,2,3 4

1,2 3,4

1,2,3 4

1,2,3 C = N dipole in site 4
Table 4.2 Estimation of polarization and piezo- and pyroelectric

coefficients for PVF 2 assuming 50% crystallinity and

33% switching efficiency and highest experimental values.

Estimate Experimental Reference

P (yC/cm

2

) 3.7 2-4 [4.11,16,30

p (HC/cm

2 -K) 2.7 4 [4.19]

d (pC/N 23 14 [4.84]

d

31 ( P C/N 20 20 [4.85]
figure Captions

Figure 4.1 A diagram of a poling procedure showing the temperature T,

voltage 5, tine t sequence and the resulting polarization P

reduced by the permittivity of free space z and applied

o field E . The remaining frozen-in reduced polarization is

the difference between dielectric constants, e at the tv?o

ei_pera uures ^a^.— «

Figure 4.2 A model of an electret with real charges and preferentially

ordered dipolar charges resulting from the applied voltage ~ .

Figure 4.3 A model of an electrer with a sheet of real charge embedded

in it and induced charges on the short circuited electrodes.

The z are the surface charge densities located at the various

positions, o, x and s.

Figure 4.4 Schematic diagram showing the principles of an electret microphone,

Figure 4.5 A model of a dipolar electret showing the flow of charge resulting

from a thickness change due to an increase in pressure or a

decrease in temperature.

Figure 4.6 A model showing how the electret of Fig. 4.5 is used for a pyroelectric apnlication. Note the interaction of the film with the

radiation takes place in the electrode which in turn acts as a

heat bath.

Figure 4.7 A model for an electret containing a representative dipole of

-cr.er.c _ , rolarizabilirv :• . ar.d fixef near, rrierrarirr t vith

o

r

respect to the net polarization P

.
Figure 4.8 A model showing the decrease in the mean moment of a librating

dipole with a temperature- induced increase in the libration

amplitude.

Figure 4.9 The identification of axies for a stretched and poled polymer specimen,

Figure 4.10 Basic molecular structure of some piezoelectric polymers. Various

polymers are identified in Table 4.1. According to the kinds

of atoms located at sites 1 thru 4.

Figure 4.11 Model for bulk samples of PVF and PVF ^ prepared under different

crystallization conditions.

Figure 4.12 Projections on a plane normal to the molecular axies of the

a, 8 and y crystal forms of PVF^.

Figure 4.13 Schematic diagram of interfacial polarization in a semicrystalline

polymer in an applied dc field due to charge build up at

crystalline obstructions.
Fife M.I
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NBS-1 14A (REV 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUB1.K ATI ON OR Kl PORT NO. NBSIR 75-787

2. C my 't Ai i ess i on

N.,. 3. Ri i ipient ' s Aceession No.

4. n i l.

i

; a nii stnvn n.i Piezo- and Pyroelectric Properties of Electrets

5. Puhl icat ion 1 lai c- uctooer

6. Performing Organization < ode

7. AUTHOR(S)

Martin G. Broadhurst and G. T. Davis

8. Performing Organ. Report No. NBSIR 75-787

9. PERFORMING ORGANIZATION N AMI-" AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/ Task/ Work Unit No.

1 1 . < orjlract 'Oram No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Office of Naval Research

Arlington, Va. 22044

13. Type of Report & Period

' :w "

" d Final

Jan. 1 Dec. 31, 1975

14. Sponsoring Agency ( ode

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) A model for piezo- and pyroelectricity in polymers is presented. These

effects are true piezo- and pyroelectricity rather than electrostriction, conduction

electromechanical effects or the motion of conductors in the field of space charges.

Two distinct types of polymers can be piezoelectric. Amorphous polymers are piezoand pyroelectric by virtue of a non-equilibrium but kinetically stable net dipole

orientation. The semicrystalline polymers are piezoelectric due to alignment of

polar, ferroelectric crystals dispersed in the amorphous phase. In both types the

magnitudes of the piezo- and pyroelectric effects are in accord with the expected

temperature and pressure dependence of the dipolar polarization. Space charges

embedded in the polymer normally will not produce a piezo- or pyroelectric current.

Those embedded near the crystal-liquid interfaces tend to reduce the piezo- and

pyroelectricity. Improved orientation of dipoles and reduction of ionic impurities

should increase p and d for PVF2 by a factor of three above typical values presently reported. The sensitivity of amorphous polymers is limited mainly by dipole

moment per unit volume and breakdown strength.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Electrets; piezoelectricity; polarization; polymers;

polyvinylchloride ; polyvinylf luoride ; polyvinylidenef luoride

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